An object with a mass of #4 kg# is acted on by two forces. The first is #F_1= < -7 N , 4 N># and the second is #F_2 = < -3 N, -2 N>#. What is the object's rate and direction of acceleration?

1 Answer
May 5, 2016

The first force vector acting on the object of mass #m=4kg# is given by #vecF_1=(-7hati+4hatj)N#

The 2nd force vector acting on the object of mass #m=4kg# is given by #vecF_2=(-3hati-2hatj)N#
So the resultant force
#vecF=vecF_1+vecF_2=((-7-3)hati+(4-2)hatj)N=(-10hati+2hatj)N#

So the acceleration
#veca=vecF/m=1/4(-10hati+2hatj)m/s^2##=1/2*(-5hati+hatj)m/s^2#

Hence the magnitude of acceleration is
#a=sqrt((-5/2)^2+(1/2)^2)=sqrt26/2m/s^2#

And its direction is #tan^-1(-1/5)# with the X-axis.